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Hypothesis: The likelihood covariance for the "virtual observations" scales linearly with the 2D likelihood variance.

Experiment: see experiments/exp_2013_07_21_likelihood_covariance.m. Constructs a likelihood using noise_variance of one and then scaling precisions afterward. Compares to directly-constructed likelihood precisions.

Results: Negligible difference

Conclusion: Practice matches theory--scaling likelihood precisions is equivalent to constructing likelihood with the scaled precision.

Discussion: This conclusion means that we can construct the likelihood precisions exactly once during training, and simply scale them as we modify the likelihood precision. It would make sense to always use 1.0 when computing precisions, and refactor all existing code to scale the matrix by the reciprocal of the noise variance before using it.

TODO

Build training framework

fast likelihood evalautor

custom function for evaluating ML without recomputing stuff

cache the three prior component matrices (smooth, linear, and offset)

cache unscaled likelihood precision.

wrap in a lambda

scales and combines all components

depending on motion model, use different expression for purturbation coefficient